This paper focuses on transmission congestion issues that are currently experienced in the electricity market of the Great Britain. It analyses the nature of incentives and behavior of generators arising in presence of persistent congestion patterns due to constraint management approach employed in the GB market. Although congestion in the GB market is often related to generators exercising market power, we demonstrate that this is not necessarily so. The observed behavior of generators is consistent with rational behavior of generators having no market power when congestion patterns become persistent. Incentives for such behavior are created by the re-dispatch type of congestion management approach used in the GB electricity market. Even though such incentives could be competitive, they have adverse consequences on market outcomes. They can be mitigated by a comprehensive modification of the market organization. In particular, market designs integrating energy market with congestion management using locational clearing prices seem at this point the most efficient approach in dealing with congestion. Several electricity markets have opted for this market design after having faced congestion issues similar to those currently experienced in the GB. Modifications currently envisaged in the GB electricity market to resolve the problem, such as the introduction of Market Power License Condition, Transmission Access Review and the locational BSUoS, may not turn out to be adequate, providing at best an imperfect and temporary solution but not necessarily an integrated and robust approach.